Epitaxial growth of inch-scale single-crystal transition metal dichalcogenides through the patching of unidirectionally orientated ribbons

Two-dimensional (2D) semiconductors, especially transition metal dichalcogenides (TMDs), have been envisioned as promising candidates in extending Moore’s law. To achieve this, the controllable growth of wafer-scale TMDs single crystals or periodic single-crystal patterns are fundamental issues. Herein, we present a universal route for synthesizing arrays of unidirectionally orientated monolayer TMDs ribbons (e.g., MoS2, WS2, MoSe2, WSe2, MoSxSe2-x), by using the step edges of high-miller-index Au facets as templates. Density functional theory calculations regarding the growth kinetics of specific edges have been performed to reveal the morphological transition from triangular domains to patterned ribbons. More intriguingly, we find that, the uniformly aligned TMDs ribbons can merge into single-crystal films through a one-dimensional edge epitaxial growth mode. This work hereby puts forward an alternative pathway for the direct synthesis of inch-scale uniform monolayer TMDs single-crystals or patterned ribbons, which should promote their applications as channel materials in high-performance electronics or other fields.

T wo-dimensional (2D) semiconducting transition metal dichalcogenides (TMDs) have attracted tremendous interest for their broad-range applications in electronics, optoelectronics, catalysis, etc. [1][2][3] . The morphology or dimensionality of TMDs is a critical factor to determine their physical properties. For instance, one-dimension (1D) monolayer MoS 2 ribbon is predicted to possess novel properties such as metallic edge states 4 , 1D confined plasmons 5 , ferromagnetic behaviors 6 , etc. Besides, it can present improved catalytic property in hydrogen evolution reaction (HER) due to the abundant active edge sites 7 , and more importantly, maintained high carrier mobility 8 . So far, the fabrication of monolayer TMDs ribbons has largely depended on micro-nanofabrication approaches, by using electron beam or optical lithography patterning techniques 9 . However, these top-down methods are evidently tedious and usually need to start with large-area uniform continuous films or crystals.
Recently, several strategies have been developed for the direct synthesis of monolayer TMDs ribbons 10 , such as Na-Mo-O droplets driven growth on NaCl single crystals 11 , substratedirected synthesis on phosphine pre-treated Si(001) substrates 12 , as well as ledge-directed epitaxy on β-Ga 2 O 3 (100) 13 . These strategies have individually achieved the control of their thickness, orientation and dimensionality, nevertheless, the synthesis of TMDs ribbons possessing all the above advantages has not been realized.
Wafer-scale monolayer TMDs single crystals, characterized by intrinsically high crystallinity and extremely uniform property, have long been pursued. However, due to the noncentrosymmetric structures of TMDs, antiparallel domains and twin boundaries usually evolved on most growth substrates [14][15][16] , similar to those encountered in the preparation of h-BN. Lately, wafer-scale growth of monolayer h-BN single crystal was achieved by using liquid Au as substrate via the self-collimation of circular h-BN grains 17 . Wafer-scale monolayer h-BN single crystals were also realized on Cu(110) 18 and Cu(111) 19 substrates, where the nucleation and growth of h-BN domains were dominantly guided by the substrate-step edges. Very recently, our group realized the epitaxial growth of inch-scale monolayer MoS 2 single crystals on Au(111) films 20 , demonstrating the potential for the unidirectionally oriented growth of TMDs grains. Despite these achievements, the successful attempts regarding the growth of wafer-scale monolayer TMDs single crystals on Au substrates remain very limited 21,22 . Meanwhile, the step-edge-guided growth of single-crystal TMDs has also been explored on insulating sapphire substrates [23][24][25][26] . Particularly, inch-scale singlecrystal MoS 2 and WS 2 monolayers have been achieved on C-A and A plane sapphire substrates, in which the nucleation of MoS 2 and WS 2 are along the <10 10> step edges of sapphire, further proving the effect of step edges on the alignment of TMDs domains. However, the direction of the step edge on sapphire is highly dependent on the miscut direction, and it is rather difficult to maintain a fixed cutting angle with such a high accuracy (e.g.,1°) over an inch scale.
Herein, we design a substrate-step templated growth strategy for synthesizing large-area uniform, unidirectionally aligned, monolayer single-crystal TMDs ribbons, by using the step edges of vicinal Au(111) single crystals as growth fronts. The superiorities of this route are summarized as follows: (1) the uniformly oriented step edges on high-index Au facets can trigger the anisotropic growth of TMDs, and direct the alignment of the resulted monolayer ribbons; (2) the chemical inertness of Au substrate to chalcogen precursor makes it a universal template for synthesizing various monolayer TMDs ribbons (e.g., MoS 2 , WS 2 , MoSe 2 , WSe 2 ); (3) different from the growth on insulating substrates, the monolayer TMDs grown on Au metals are featured with relatively strong interface coupling, which can be another parameter for mediating the van der Waals epitaxial growth of 2D layered materials toward wafer-scale single crystals; (4) the synergistic effect of substrate-step-edge guided 1D epitaxy, combined with substrate-lattice-match directed 2D epitaxy modes are expected to direct the epitaxial growth of single-crystal TMDs monolayers. This work is expected to offer an alternative strategy for the synthesis of monolayer patterned TMDs ribbons or waferscale single-crystal films. The practical applications of the dimension controllable monolayer materials (ribbons or films) will also be demonstrated in more versatile fields, e.g., as channel materials in high-performance electronic devices and as catalysts in HER.

Results
Theoretical calculations for the evolution of monolayer TMDs ribbons. To initialize the growth of monolayer MoS 2 ribbons, it is a general route to introduce anisotropic template with broken symmetry, e.g., by introducing substrate steps 27 . Such a substratetemplate-directed synthesis strategy has previously been used for the growth of 1D GaN 28 , graphene 29 , and MoS 2 nanowires 30 . In our experiment, a series of high-miller-index Au facets vicinal to (111) with bunched atomic steps were selected as growth templates, as obtained by melting and resolidifying Au foils on W templates (see Methods for more details). As reported previously, the types of the MoS 2 terminated edges were quite different for 1D stripes and 2D triangles, i.e., Mo-zigzag (Mo-zz)/S-zigzag (S-zz) edges and Mo-zz edges, respectively, as characterized by transmission electron microscope (TEM) in previous literatures 27,28 . Moreover, the edge type of monolayer MoS 2 achieved by the CVD growth process highly depended on the S/ Mo ratio of precursors [31][32][33][34] . In this regard, the effect of S/Mo ratio should have a significant effect on the morphology of monolayer MoS 2 .
To confirm this, CVD growth was executed on a representative Au(223) facet with MoO 3 and S as precursors (growth conditions: 750°C for 3 min, Supplementary Fig. 1). When the mass ratio of S/Mo was set at 3:1, monolayer MoS 2 triangular domains were obtained (Fig. 1b). As the S/Mo ratio decreased to 2:1, monolayer MoS 2 ribbons evolved under similar growth conditions (Fig. 1c). X-ray photoemission spectroscopy (XPS) spectra confirmed the formation of MoS 2 compounds ( Supplementary Fig. 2). Atomic force microscope (AFM) images of as-grown monolayer MoS 2 triangular domains and ribbons on Au substrates ( Supplementary  Fig. 3) clearly show that the edges of MoS 2 are usually aligned along the steps of Au substrates, providing straightforward evidence for the step-edge-guided growth mechanism. Nevertheless, further decreasing the S/Mo ratio to 1:1 led to the formation of irregularly shaped MoO x S 2−x crystals (Supplementary Fig. 4), probably due to the insufficient feeding of the S feedstock 30 .
To further understand the role of S/Mo ratio in the morphological evolution of monolayer MoS 2 , density functional theory (DFT) calculations were then performed to simulate the MoS 2 growth on Au(111). The kinetic growth of MoS 2 can be analyzed by exploring the nucleation barriers of two dominating edges on Au(111) around <110> step during the atomic accretion process, i.e., S-zz and reconstructed Mo-terminated zigzag (Mo'zz) edges due to their higher nucleation barriers than those of armchair, and Mo-zz (see details in Supplementary Figs. 5-7). Using Mo atoms and S 2 dimers as the feeding units, the relative nucleation barriers (ΔE) for these two edges under different chemical potentials of Mo and S (labeled as μ Mo and μ S , respectively) were calculated. For the case of high μ S and low μ Mo (bottom right in Fig. 1d), the nucleation barriers of S-zz are smaller than that of Mo'-zz edges (ΔE < 0). Hereby, Mo-oriented edges should be prevalent in parallel with the evolution of triangular-shaped domains. As μ S decreases (ΔE > 0, bottom left in Fig. 1d), the growth velocity of S-zz edge declines significantly, and S-zz edge becomes the dominating one. Following our previous results 20 , the minimum energy configuration corresponds to Mo-zz edges docking to Au <110> steps on the (111) surface. Thereby, the ribbons terminated with Mo-zz edges along the Au <110> steps (on one side) and terminated with free S-zz edges on the terraces (on the other side) should be more preferentially evolved. The schematic diagram in Fig. 1e depicts the shape evolutions of MoS 2 from triangles to isosceles trapezoid or quasi stripes with the change of S/Mo ratios.
Controllable growth of uniformly aligned monolayer TMDs ribbons. According to our theoretical calculations, the following mechanism is proposed for the formation of unidirectionally oriented monolayer MoS 2 ribbons. As schematically illustrated in Fig. 2a, MoS 2 species tend to first nucleate at the step edges on the high-miller-index Au facets, considering of the high binding energy between them. Under a relatively small S/Mo ratio, the growth rate of S-zz edge was slower than that of Mo-zz edge, inducing the formation of MoS 2 ribbons terminated by Mo-zz and S-zz edges on either side.
Raman and photoluminescence (PL) spectra were then collected from the monolayer MoS 2 ribbons transferred on SiO 2 /Si substrates. The Raman characteristic peaks are fixed at 386 cm −1 (E 1 2g ) and 406 cm −1 (A 1g ) ( Fig. 2d), with a frequency difference (Δ)~20 cm −1 , justifying the monolayer nature of the MoS 2 ribbons 37 . However, the Raman intensity of the ribbon edge is slightly lower than that of the center region ( Fig. 2e), probably due to the reduced electron density at the ribbon edge. Meanwhile, the PL spectrum from the ribbon edge exhibits a blue-shifted peak (at~677 nm) and lower intensity ( Fig. 2g) relative to the center region (at~684 nm), which may arise from the strain at the ribbon edge 38,39 .
More intriguingly, such step-edge-guided growth of monolayer MoS 2 ribbons was also realized on monolayer graphene or h-BNcovered vicinal Au(111) facets. As shown in Fig. 2i, well-aligned monolayer MoS 2 ribbons occurred on a monolayer graphenecoated Au(213) facet, as confirmed by the coexistence of characteristic Raman signals for monolayer MoS 2 , i.e., E 1 2g (~386 cm −1 ) and A 1g (~406 cm −1 ) peaks, and graphene on the same region ( Supplementary Fig. 10). Besides, patterned monolayer MoS 2 ribbons were also achieved on the monolayer h-BN/ Au(111) template ( Supplementary Fig. 11). The compatibility of Au substrate with the growth of TMDs, graphene, and h-BN makes it possible to construct van der Waals heterostructures based on these 2D layered materials.
Apart from monolayer MoS 2 , monolayer TMDs alloys ribbons, such as MoS x Se 2-x , were also achieved on an Au(235) facet by using mixed S and Se as chalcogen precursor (Fig. 2k). Raman spectrum (inset of Fig. 6g) shows two groups of characteristic peaks, in line with that of MoS 2 (at~386 and 405 cm −1 ) and MoSe 2 (at~270 cm −1 ), justifying the formation of MoS x Se 2-x compounds 40 . Given these facts, the substrate-step-edge guided growth route can be utilized as a universal pathway for the growth of TMDs ribbons and their alloys.
Preparation of inch-scale high-miller-index Au single-crystal films.
The key point of this synthetic route relies on the preparation of anisotropic substrate of vicinal Au(111) single-crystal facets. To achieve this, Au foils on W templates were melted and resolidified at~1100°C and maintained for~20 min. The schematic and photograph of a representative Au film (with a size of 3 cm × 3 cm) featured with Au(223) facet are presented in Fig. 3a, b, respectively. The facet surface was characterized by uniformly distributed, parallel bunched steps, as evidenced by the AFM image in Fig. 3c. X-ray diffraction (XRD) pattern of the asprepared Au/W film shows the (111) peaks of Au film, and the (200) and (211) peaks of W foil (Fig. 3c).
However, due to the limited resolution of XRD, it is difficult to distinguish the exact miller-index of the Au facet. Further electron backscatter diffraction (EBSD) characterization reveals the evolution of such a single-crystal Au(223) facet (Fig. 3d). Large-area EBSD maps collected on the whole sample surface show uniform color contrast and nearly undetectable angular variation ( Supplementary Fig. 12), confirming the single crystallinity of the Au(223) facet. Notably, a series of single-crystal Au(111) vicinal facets were also achieved through the current annealing process, including (235), (213), (346), (456), etc. (Fig. 3d and Supplementary Fig. 13), as defined by the homogeneous color contrasts in the inverse pole figure maps.
The derived high-miller-index Au facets belong to a category of facets vicinal to Au(111), which are composed of a regular succession of (111) terraces separated by monatomic steps. Notably, the appearance of a specific high-index facet is relatively random, as similarly proposed in the preparation of atomic sawtooth high-miller-index Au facets through different annealing processes 21 . Herein, the formation of the high-index facet is probably due to the close contact between Au liquid and W template at high temperature, in which the strain energy should be the driving force, rather than the surface energy for the formation of Au(111). This phenomenon was also reported in the preparation of high-miller-index single-crystal Cu foils, in which the stress on Cu foil was introduced by using graphite susceptor 41 . Notably, a variety of vicinal Au(111) facets, independent of the specific index (e.g., Au(456), Au(346)), were all proved to be capable of inducing the formation of monolayer MoS 2 ribbon arrays (Fig. 3e, f). Besides, the as-grown monolayer MoS 2 ribbon presents a relatively high density on the high-millerindex Au facet with a high density of step ( Supplementary  Fig. 14). This provides an effective route for ribbon density regulation.
Monolayer TMDs single-crystal films merged by 1D ribbons. The lateral growth and merging behavior of monolayer TMDs     substrate (yellow circles). The uniform diffraction pattern that appeared on the inch-scale sample should indicate the epitaxial growth of monolayer MoS 2 single crystal on the Au(223) facet ( Fig. 4f and Supplementary Fig. 15). TEM and scanning transmission electron microscopy (STEM) characterizations were then conducted to identify the lattice orientation and edge structure. A representative atomically resolved STEM image presents well-ordered honeycomb lattices (Fig. 4h). On large scales, the crystal lattice of MoS 2 maintains the same orientation, showing almost no obvious grain boundary. Selected-area electron diffraction (SAED) patterns collected on the film (Supplementary Fig. 16) reveal nearly identical lattice orientation (deviation smaller than ±0.1°), highly indicative of the single-crystal nature of the MoS 2 film. Moreover, the edge types on both sides of the monolayer MoS 2 ribbon are identified as Mozz and S-zz edges from both SAED pattern ( Supplementary  Fig. 17) and atomic-resolution STEM image (Fig. 4i), and this result is consistent with our previous calculations. Dark-field TEM images of the monolayer MoS 2 film show uniform intensity over the entire area, again confirming its single crystallinity ( Supplementary Fig. 18).
On-site scanning tunneling microscopy (STM) measurements were then performed to determine the crystalline quality. A largearea STM image reveals the covering of a continuous monolayer MoS 2 film on the Au(111) terraces (Fig. 5a). Further magnified image (from the region marked by the green square in Fig. 5a) presents the evolution of a large-area hexagonally shaped moiré pattern with a period of ∼3.21 ± 0.10 nm (Fig. 5b). Moreover, the orientation of the MoS 2 atomic row aligns well with the moiré row direction (as denoted by green and yellow arrows, respectively). This alignment was also confirmed by the corresponding 2D fast Fourier transform image (inset of Fig. 5b), indicating an epitaxial relationship between them. As calculated, the moiré supercell (highlighted by a white rhombus) is in line with a (10 × 10) supercell of MoS 2 (a 1 = 0.320 nm) on an (11 × 11) supercell of Au(111) (a 2 = 0.288 nm). Furthermore, atomic-resolution STM images collected from the entire film show the same lattice orientation (Fig. 5b-d and Supplementary   Fig. 19), highly indicating the single-crystal nature of the monolayer MoS 2 film.
Further photograph and optical microscopy (OM) images reveal homogenous color contrasts for the 1-inch single-crystal MoS 2 film transferred on SiO 2 /Si (Fig. 5e). Additional Raman and PL intensity mappings also suggest the homogeneous optical properties (Fig. 5f, g). Moreover, almost no obvious contrast difference can be noticed in the second-harmonic generation intensity mapping (Fig. 5h), which unambiguously confirms the single crystallinity of the monolayer MoS 2 film.
Syntheses of other monolayer TMDs ribbon arrays. To further display the universality of our synthetic strategy, other TMDs ribbons and alloys, such as WS 2 , MoSe 2 , WSe 2 , and MoS x Se 2-x were also synthesized on the high-miller-index facets vicinal to Au(111) (Fig. 6a-h), by using MO 3 (M = Mo, W) and S, Se as precursors. Corresponding Raman data and STEM image confirm the desired chemical composition and monolayer nature of the ribbons.
The ready access to monolayer TMDs ribbons provides us an opportunity for exploring their exotic electronic and catalytic performances. In order to characterize their electronic properties, back-gated FETs were constructed for MoS 2 ribbons on SiO 2 /Si substrates (Fig. 6i). The transfer (Supplementary Fig. 20) and output curves (Fig. 6j) of a representative device show typical n-type transfer characteristics. Statistical data measured on these FETs ( Supplementary Fig. 21) show a narrow electron mobility distribution 7-11 cm 2 V −1 s −1 and an on/off ratio of 10 5 -10 6 , comparable to the performance of 2D MoS 2 monolayers achieved on Au substrates 20 . Notably, the performance of the FETs based on monolayer MoS 2 grown on Au are not as good as those of monolayer MoS 2 films grown on sapphire 16,28,42 . This may originate from the different sample transfer processes used for them (e.g., electrochemical bubbling transfer), wherein contamination and structural defects were usually introduced. Hereby, a more efficient and clean sample transfer process should be developed in the future. Besides the potential application as channel material, monolayer MoS 2 ribbon was also predicted to possess higher catalytic performance in HER than its 2D counterpart, owing to the exposure of more abundant active edge sites. The applications of 1D monolayer MoS 2 ribbons and 2D monolayer MoS 2 flakes grown on Au/W substrates are also addressed as electrocatalysts in HER (Fig. 6k). The overpotential (at a current density of 10 mA cm −2 ) and Tafel slope of monolayer MoS 2 ribbons were measured to be~194 mV and 56 mV dec −1 , respectively, obviously lower than the values for 2D MoS 2 flakes (~220 mV and 71 mV dec −1 ) (Fig. 6l and Supplementary Fig. 22). Moreover, the catalytic current density exhibited negligible loss (<5%) after 1000 cycles, indicating the relatively high catalytic stability. The loading of the catalysts can be further increased toward low-cost, high-efficiency, and large-scale application explorations.

Discussion
In conclusion, we have realized the direct synthesis of periodic monolayer TMDs ribbon arrays, and wafer-scale TMDs single crystals on high-miller-index Au facets vicinal to (111) via a designed step-edge-directed synthetic strategy. Monolayer TMDs ribbons characterized by strictly monolayer thickness, high aspect ratio, relatively straight edge, and uniform alignment have been achieved. Based on this, an alternative epitaxial growth approach for wafer-scale TMDs single crystals is proposed by merging these uniformly aligned monolayer ribbons through a unique 1D edgeepitaxy mode. This work hereby opens a pathway for the singlecrystal growth of 2D semiconductors on a wafer scale, as well as deepens our understanding of the epitaxial growth mechanism for the wafer-scale synthesis of 2D layered materials on insulating or conducting templates. This work should also propel the application explorations of monolayer TMDs ribbons or single crystals as channel materials in nanoelectronics and efficient catalysts in energy-related fields.

Methods
Preparation of vicinal Au(111) single crystals. The commercial polycrystalline gold foils (99.99%,~50 µm thickness) were first ultrasonic cleaned in HCl solution (20% wt) for 10 min, and then in an acetone solution for 10 min. To prepare the high-miller-index facets vicinal to Au(111), a piece of cleansed gold foil was placed on an etched tungsten foil on a graphite boat, annealing at~1100°C for 20 min with a mixture of Ar/H 2 (300/50 sccm) as the carrier gas. The gold will firstly melt into liquid at~1100°C, and resolidified to induce the formation of Au(111) vicinal facets after cooling down processes.
Synthesis of monolayer TMDs ribbons. For the growth of MoS 2 ribbons, the MoO 3 and S powders were placed in the upstream of Au(111)/W substrate at a distance of 4 and 20 cm in a three-zone tube furnace, respectively. The growth was performed in a low-pressure environment with the protection of Ar (50 sccm) gas. The typical temperatures of S, MoO 3 (2-3 mg), and Au(111) substrates were~100, 530, and~750°C, respectively. The S/Mo ratio was defined by the quantity of S and MoO 3 precursors. Notably, this growth temperature was relatively higher than  Intensity (a.u.) Raman Shift (cm -1 ) Fig. 6 Au-step-edge-directed growth of other monolayer TMDs ribbons. a, b. SEM image (a), representative Raman spectrum (inset of (a)), and STEM image (b) of as-grown monolayer WS 2 ribbon arrays. c, d SEM image (c), representative Raman spectrum (inset of (c)), and STEM image (d) of as-grown MoSe 2 ribbon arrays. e, f. SEM image (e), representative Raman spectrum (inset of (e)), and STEM image (f) of as-grown monolayer WSe 2 ribbon arrays. g, h SEM image (g), representative Raman spectrum (inset of (g)), and STEM image (h) of as-grown monolayer MoS x Se 2-x ribbon arrays. i AFM image of a representative monolayer MoS 2 ribbon-based device with a width of~110 nm. j Output characteristics of the monolayer MoS 2 ribbon-based device. k Schematic illustration of the HER process. Red and yellow spheres represent Mo and S atoms, respectively, and the black dots denote the electric charges. l Tafel plots of the as-grown monolayer MoS 2 triangles and monolayer MoS 2 ribbons on Au/W electrodes.
For the growth of monolayer WS 2 ribbons, the typical temperatures of S, WO 3 , and Au substrates were set at~100, 820, and 820°C, respectively. For the growth of 1D monolayer MoSe 2 and WSe 2 ribbons, a mixture of Ar (50 sccm) and H 2 (5 sccm) was used as the carrier gas. The Se powder was placed in the upstream of a substrate at a distance of 16 cm. The typical temperatures for Se, MoO 3 (WO 3 ), and Au substrates were set at~200, 530 (820), 820°C, respectively. For the synthesis of monolayer MoS x Se 2-x ribbons, the MoO 3 precursor and a mixed S and Se precursor were placed in the upstream of Au/W substrate at a distance of 1 and 20 cm, respectively. The typical temperatures for the Au substrates, MoO 3 , and S/Se mixture were set at 850, 800, and 200°C, respectively. The growth process was performed under a mixture flow of Ar (50 sccm) and H 2 (5 sccm) gases. The synthetic recipes for MoS 2 ribbons grown on graphene and h-BN monolayers are provided in the Supplementary information.

Data availability
The data that support the findings of this study are available from the corresponding author upon request.